Optimal control problem for fractional stochastic delayed systems with noninstantaneous impulses

This article investigates the existence of a solution for a class of fractional delayed stochastic differential equations with noninstantaneous impulses and fractional Brownian motion (fBm). Utilizing the theory of fractional calculus, stochastic integrals for fBm and fixed-point technique, we obtain the solvability result for the considered system. Next, we formulate a fractional stochastic optimal control problem for the infinite delayed impulsive system. Finally, the existence of an optimal state-control pair is established using the Balder Theorem. An example is also constructed that exhibits the efficiency of our results.